Ok..you have given me something to go on!
The fact that with egr valve connected ,you have more smoke (oil),means thats its coming from exhaust and engine is burning oil,thats why I asked you to check the oil level dipstick for any signs there of blowing smoke!

Some error codes do not bring EML on but are stored as intermitent errors ,since you dont always have the egr blocked!EGR error code is because its wasnt connected.FYI and your mechanics,the egr valve needs to be connected before any diagnostics is performed,otherwise you wont get proper readings from your MAF or pressure converter.
No problem blocking egr vacuum pipe (in fact its beneficial).You only need to connect it for doing diagnostics.

Smoke on start up only,maybe a glow plug !Have you had these checked?Could also be a dirty injector?
Can you first do the oil level dipstick test and let me know !